Question

A 15 kg bowling ball traveling at 24.5 m/s strikes a 5 kg. bowling pin that is at rest. After the collision the ball is traveling at 20 m/s. What would be the final velocity of the pin if they don't stick together? (assume no rotational motion of the ball and pin and a frictionless surface)

Answer 1

This is an example of a perfectly inelastic collision, where the ball and pin stick together and move as a single entity after the collision. In this type of collision, the total momentum of the system (ball and pin) is conserved, but the total kinetic energy is not.

To find the final velocity of the system (ball and pin), we need to use the conservation of momentum equation:

m1v1 + m2v2 = (m1 + m2)vf

where m1 is the mass of the ball, v1 is its initial velocity, m2 is the mass of the pin, v2 is its initial velocity (0 m/s, since it was at rest), and vf is the final velocity of the system.

Substituting the known values:

15 kg * 24.5 m/s + 5 kg * 0 m/s = (15 kg + 5 kg) * vf

vf = (15 kg * 24.5 m/s) / (15 kg + 5 kg) = 20 m/s

So the final velocity of the system (ball and pin) is 20 m/s. Since the ball and pin are stuck together after the collision, this is also the final velocity of the pin.